The internet is a powerful tool artists can use to market themselves. It's not complicated and only requires time and maybe a little money.
The following are four techniques an artist can use to successfully market themselves online.
1) Article marketing
If you have a specific genre of art that you primarily work with, you can write articles about it. Since you're already intimately familiar with it, you shouldn't have to conduct any research.
A lot of people avoid article marketing because they think it entails gobs of research.

If you're writing about what you already know, then you shouldn't have to do any research. Just because you don't conduct research doesn't mean it's not good writing. It's good writing because you know your subject and can communicate it well.
After you write an article, you need to submit it to an article directory. There are several very good article directories available.

Do a search for "article directory" online.
2) Digitize your art
The only way others are going to get to know you and your art is for them to see your art.
All you need is a digital camera and a website to make it work. There are also photo sharing websites that will allow you to post pictures of your art for free.
Anyone who is serious about marketing online needs to have their own website. Having a website is about creating your own brand. You can't create a brand on a photo sharing site alone.
3) Give something away
People like free stuff. In exchange for an email and name, give visitors access to a "private" collection of your art.
You may also want to put together a small ebook with your best art.

Along with pictures, you can include captions and other interesting facts.
4) Give yourself away
One of the primary reasons I tell someone to get a website is because it opens up so many more marketing channels. If you have a website, you can pass out cards with your web address (URL).
Many times, people will visit your site out of curiosity. It may not get you a targeted visitor but that single visitor may know someone with art interests.
It doesn't take much talent, computer knowledge, or a college degree to market yourself successfully online. As an artist, creativity is an enjoyable and important process. Now, all you have to do is apply that creativity to your online marketing efforts.